Six themes for QG in 2015 (developments to watch for)

[marcus]

something nice is happening here that has to do with conjugate variables like position and momentum.
if one of a pair is bounded, has a maximum measurable size, then the other partner has to have a minimum measurable size.

It would be great if someone wants to explain more clearly. they seem to be saying that building a small positive curvature in, a maximum radius of curvature, gives you a minimum measurable length. Phase space compactness gives, in effect, cutoffs.

It reminds me of the 2013 HR and CHR papers where the phase space has a kind of fuzzy discreteness and TIME is ticked off in intervals which are how long it takes for the system to change to a different state. The rate that time passes is the rate that the system undergoes change. 2013 HR was a fascinating paper because in a General Covariant picture you cannot define "equilibrium" in the conventional way --because of the Tolman effect two systems can be in contact but measure different temperatures because of a difference in gravitational potential! So gravitational time dilation must balance the temperature difference---changes happen slower but higher temp compensates, in the deeper system. In that paper proper time was represented physically as hopping from one state to the next in a semi-discrete phase space. This new "Compact Phase Space" paper chimes with the HR/CHR. So I will recall the abstracts to have it handy if anyone wants to check it out.

First this one
http://arxiv.org/abs/1302.0724
Death and resurrection of the zeroth principle of thermodynamics
Hal M. Haggard, Carlo Rovelli
(Submitted on 4 Feb 2013)
The zeroth principle of thermodynamics in the form "temperature is uniform at equilibrium" is notoriously violated in relativistic gravity. Temperature uniformity is often derived from the maximization of the total number of microstates of two interacting systems under energy exchanges. Here we discuss a generalized version of this derivation, based on informational notions, which remains valid in the general context. The result is based on the observation that the time taken by any system to move to a distinguishable (nearly orthogonal) quantum state is a universal quantity that depends solely on the temperature. At equilibrium the net information flow between two systems must vanish, and this happens when two systems transit the same number of distinguishable states in the course of their interaction.
5 pages, 2 figures

And then this:
http://arxiv.org/abs/1309.0777
Coupling and thermal equilibrium in general-covariant systems
Goffredo Chirco, Hal M. Haggard, Carlo Rovelli
(Submitted on 3 Sep 2013)
A fully general-covariant formulation of statistical mechanics is still lacking. We take a step toward this theory by studying the meaning of statistical equilibrium for coupled, parametrized systems. We discuss how to couple parametrized systems. We express the thermalization hypothesis in a general-covariant context. This takes the form of vanishing of information flux. An interesting relation emerges between thermal equilibrium and gauge.
8 pages, 3 figures

There was an earlier thread about these two:
https://www.physicsforums.com/threa...ynamics-paper-says-what-time-is.669658/page-3

 

[marcus]

This theme#2 paper is intriguing partly because of the diverse concepts it pulls together. One of the things is that quantum nature has a smallest positive detectable angle and this is related to the cosmological curvature constant. Eugenio Bianchi wrote a paper with Rovelli about that in 2011. It comes up in the "Compact phase space paper"!
It somehow makes sense that a smallest measurable angle should have something to do with the intrinsic spacetime curvature, that you can't get away from. A vacuum curvature constant inherent in geometry. Angle?, curvature? aren't they somehow related? :D :D

Theme #2 (recall the HHKR paper, LQG with constant curvature simplexes to embody Λ)!
The authors here, in their acknowledgment, thank Haggard and Han, and say the present work was directly inspired by the intrinsic curved simplices approach developed by HHKR to embody the cosmological [curvature] constant.
http://arxiv.org/abs/1502.00278
Compact phase space, cosmological constant, discrete time
Carlo Rovelli, Francesca Vidotto
(Submitted on 1 Feb 2015)
We study the quantization of geometry in the presence of a cosmological constant, using a discretization with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to discreetness of time, in addition to space. We work in 2+1 dimensions, but these results may be relevant also for the physical 3+1 case.
6 pages

This will definitely be presented and discussed at the EFI Winter School meeting in the mountains at Tux Austria this month (13-20 Feb).

Fun paper. A lot going on here. Could turn out to be one of 2015's most important papers. Since the cosmological constant is a small CURVATURE, a kind of inherent "vacuum curvature"which geometry has, it is not proper to represent it in a theory with FLAT simplexes, the authors say. So they employ Haggard Han Kaminski Riello formulation (http://arxiv.org/abs/1412.7546) that uses simplices with a slight uniform built-in curvature. The cosmological constant becomes inherent in the tools. That is what theme #2 was about. It is nice to see a paper following this lead so soon!

This is an amazing paper. It is conceptually not too complicated but it pulls together a number of ideas: a minimal nonzero measurable angle, a minimal measurable time interval, a maximal acceleration. Also a kind of conjugate momentum of the geometry so that one can describe a phase space namely the state of the geometry together with its conjugate momentum, whereupon this phase space turns out to be compact. The authors say to expect a related paper by Haggard Han Kaminski Riello to appear soon, dealing with the dimension 3+1 case. Vidotto will be giving a talk based on this "compact phase space" paper this month at the EFI Winter School
http://www.gravity.physik.fau.de/events/tux3/tux3.shtml
http://www.gravity.physik.fau.de/events/tux3/tux3.shtml

The 2011 Bianchi Rovelli paper was http://arxiv.org/abs/1105.1898
A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity
Eugenio Bianchi, Carlo Rovelli
(Submitted on 10 May 2011)
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We consider here a different geometrical interpretation of this cut-off, where the relevant non-commutative space is the space of directions around any spacetime point. The limitations in angular resolution expresses the finiteness of the angular size of a Planck-scale minimal surface at a maximum distance 1/\sqrt{\Lambda}related the cosmological constant Lambda. This yields a simple geometrical interpretation for the relation between the quantum deformation parameter q=exp[i \Lambda l_{Planck}^2 ] and the cosmological constant, and resolves a difficulty of more conventional interpretations of the physical geometry described by quantum groups or fuzzy spaces.
3 pages, 1 figure Phys.Rev. D84 (2011) 027502

For readers who might be unfamiliar the cosmological curvature constant that appears in the Einstein GR equation is not an "energy" of some strange sort, it is a curvature, i.e. a reciprocal area.
One over length squared. If the curvature is small the length is large. In simple cases it is the radius of curvature of the curvature.
That's the distance 1/\sqrt{\Lambda} that appears in the above abstract.

 

[marcus]

some excerpts from the "compact phase space" paper
==quote http://arxiv.org/abs/1502.00278 ==
A discretization of spacetime in terms of flat simplices is not suitable for a theory with cosmological constant be- cause flat geometry solves the field equations only with vanishing cosmological constant. This problem can be solved choosing a discretization with simplices with con- stant curvature. Here we show with a positive cosmolog- ical constant, a constant curvature discretization leads to a modification of the LQG phase space. The phase space turns out to be compact for each link. The conventional LQG phase space is modified by curving the conjugate momentum space. ...not the momentum space of a particle to be curved, but rather the space of the conjugate momentum of the gravitational field itself. We study the quantization of the resulting phase space, and we write explicitly modified quantum geometrical operators ...
...
...A compact phase space is the classical limit of a quantum system with a finite dimensional Hilbert space. This can be seen in many ways; the simplest is to notice that a compact phase space has a finite (Liouville) volume, and therefore can accommodate a finite number of Planck size cells, and therefore a finite number of orthogonal quantum states. The familiar example of quantum system with finite dimensional Hilbert space is given by angular momentum, for systems with fixed total angular momentum, where the quantum state space is the Hilbert space Hj that carries the spin-j representation of SU(2).

In standard LQG, the kinematical data are given by an element of Γ ≡ su(2) × SU(2) on each link. Γ is the phase space of the theory, for each link. Since it is a a cotangent space, it carries a natural symplectic structure. The corresponding quantization defines the quantum theory of gravity in the loop representation. This is defined on the Hilbert space L₂[SU(2)], where the group elements act multiplicatively and the algebra elements act as left invariant vector fields. Here we want to modify this structure by replacing the algebra su(2) with the group SU(2). The problem we address is therefore to determine the phase space structure of SU(2) × SU(2) and its quantization. ...
==endquote==
Conceptually (*waves hands*) the point is that su(2) is like a tangent space at the identity to SU(2). If it is deformed by momentum space curvature it can itself become SU(2). Then the phase space is SU(2)xSU(2) and compact.

 

[marcus]

The talk titles and abstracts from the Erlangen Cosmology and QG workshop have been posted, which hadn't happened yet when I posted about it earlier:

... two relevant meetings coming up in February
Cosmology and Quantum Gravity Workshop (Erlangen, 9-13 February)
EPI Winter School in Quantum Gravity (Tux, 16-20 February)
http://www.gravity.physik.fau.de/events/cosmo2015/cosmo2015.shtml
http://www.gravity.physik.fau.de/events/tux3/tux3.shtml
http://www.gravity.physik.fau.de/events/tux3/tux3.shtml

Last week when the program for Tux was posted I noticed that FOUR of the six themes will serve as topics of invited talks (2,3,4, and 6)

Talk titles for the Cosmology&QG workshop have not been posted, but Edward Wilson-Ewing is one of the invited speakers listed, so there will likely be a talk on LambdaCDM bounce cosmology.
Another of the speakers at the workshop is Latham Boyle who has recently co-authored papers on topic 1 of our list (spectral geometry and the standard model: "algebraic geomatter").
There is at least a chance he will discuss that during his participation in the workshop.

In fact Latham Boyle's talk WAS about theme #1.
The abstract is here (scroll down):
http://www.gravity.physik.fau.de/events/cosmo2015/cosmo2015-prog.shtml
==excerpt==
Speaker: Latham Boyle
Title: Rethinking Connes' Approach to the Standard Model of Particle Physics via Non-Commutative Geometry
Abstract: Connes' notion of non-commutative geometry (NCG) generalizes Riemannian geometry and yields a striking reinterpretation of the standard model of particle physics, coupled to Einstein gravity. I will start with a gentle introduction to his approach and the physical reasons to be interested in it. I then explain our recent reformulation, which has two key mathematical advantages: (i) it unifies many of the traditional NCG axioms into a single one; and (ii) it immediately generalizes from non-commutative to non-associative geometry. Strikingly, it also resolves a long-standing problem plaguing the NCG construction of the standard model, by precisely eliminating from the Lagrangian the collection of 7 problematic terms that previously had to be removed by an ad hoc assumption. ...
... This extension has phenomenological and cosmological implications,...
==endquote==
As one might have expected there was also a theme#4 LambdaCDM Bounce Scenario talk by Wilson-Ewing

Two more Erlangen talks showed the growing interest in LQC's observational consequences:
Speaker: Abhay Ashtekar
Title: Pre-inflationary dynamics in LQC: Interplay between theory and Observations
and
Speaker: Ivan Agullo
Title: Phenomenological consequences of LQC
==excerpt==
Abstract: Loop quantum cosmology has become a robust framework to describe the highest curvature regime of the early universe. This talk will describe explore the phenomenology of this framework. We will discuss the parameter...
==endquote==

 

[marcus]

The 2009 Bahr Dittrich paper about embodying the cosmological curvature constant in a simplicial theory by baking it into the very simplices one is using could be seen as crucial because it broached the idea which e.g. Rovelli and Vidotto followed up on just now in 2015 by observing that in the LQG context it leads to a compact phase space.
So I'll insert the 2009 abstract here for convenient reference.
http://arxiv.org/abs/0907.4325
Regge calculus from a new angle
Benjamin Bahr, Bianca Dittrich
(Submitted on 24 Jul 2009)
In Regge calculus space time is usually approximated by a triangulation with flat simplices. We present a formulation using simplices with constant sectional curvature adjusted to the presence of a cosmological constant. As we will show such a formulation allows to replace the length variables by 3d or 4d dihedral angles as basic variables. Moreover we will introduce a first order formulation, which in contrast to using flat simplices, does not require any constraints. These considerations could be useful for the construction of quantum gravity models with a cosmological constant.
8 pages

 

[marcus]

Maybe I erred in identifying these 6 themes as especially interesting to watch for developments in. I want to check the 6 I picked out earlier against the titles of the talks at Tux last week. The EFI workshop ended on 20 Feb. Let's see if I can copy the program's list of talks here so we can scan it and see what stands out. I've highlighted some of those that caught my attention. There are a lot of interesting themes here, including several that go beyond the 6 identified earlier. In the case of some talks, like the first one here on "quantum enumerative geometry" I simply could not guess what they might be about:
http://www.gravity.physik.fau.de/events/tux3/tux3.shtml

Piotr Sulkowski:
Chern-Simons theory and quantum enumerative geometry

Mehdi Assanioussi:
Construction of a hamiltonian operator in LQG

Beatriz Elizaga:
Effective homogeneous and isotropic scenarios emerging from states of the hybrid Gowdy model

Maciej Dunajski:
Non-relativistic twistor theory and Newton-Cartan geometry

Giuseppe Sellaroli:
Spinor operators in 3D Lorentzian gravity

Muxin Han:
Chern-Simons Theory, Flat Connections and 4d Quantum Geometry

Marcin Kisielowski:
First-order Dipole Cosmology

Guillermo Mena Marugan:
Mukhanov-Sasaki equations in Loop Quantum Cosmology

John Schliemann:
Coherent Quantum Dynamics: What Fluctuations Can Tell

Ilkka Mäkinen:
Coherent state operators in loop quantum gravity

Ivan Agullo:
Phenomenological consequences of LQC

Tomasz Pawlowski:
Interfacing loop quantum gravity with cosmology

Edward Wilson-Ewing:
A Lambda-CDM Bounce Scenario

Andrzej Dragan:
Ideal clocks - convenient fiction

Goffredo Chirco:
Statistical mechanics for general covariant systems

Martin Ammon:
Recent developments in AdS/CFT and higher spin gravity

Jorge Pullin:
Recent results in spherically symmetric LQG

Mercedes Martin-Benito:
More information about the early Universe than meets the eye

Carlo Rovelli:
Can we test quantum gravity with black hole explosions?

Benjamin Bahr:
Background-independent renormalization in Spin Foam models

Maite Dupuis:
Towards the Turaev-Viro amplitudes from a Hamiltonian constraint

Maximillian Hanusch:
Symmetry Actions and Invariance Conditions in LQG

Xiangdong Zhang:
Loop quantum cosmology in 2+1 dimensions

Simone Speziale:
First order gravity on the light front

Wolfgang Wieland:
New action for simplicial gravity: Curvature and relation to Regge calculus

Florian Girelli:
The Turaev-Viro amplitude from a Hamiltonian constraint, Part 2.

Jedrzej Swiezewski:
Radial gauge - reduced phase space of General Relativity

Lacina Kamil:
The problem of time in background independence

Andrea Dapor:
Rainbows from Quantum Gravity

Francesca Vidotto:
The compact phase space of Loop Quantum Gravity

Norbert Bodendorfer:
A quantum reduction to Bianchi I models in LQG

Marc Geiller:
Flux formulation of loop quantum gravity

Saeed Rastgoo:
Polymerization and saddle point approximation issues in dilatonic black hole

Thirty-three talks. I find that, scanning down to see which ones "rang a bell", for whatever reason, I highlighted ten of them.

 

[marcus]

The Tux conference in February was, I think, a good indicator of active lines of QG research being pursued, and the slides for each talk are now posted.
http://www.gravity.physik.fau.de/events/tux3/tux3.shtml
So let's check it out and get an overview. I've starred the talks that especially caught my attention and which in several cases have something to do with the themes I mentioned at the start of the thread. I'll take a closer look at those marked with an asterisk. If anyone else notices other talks of particular interest, please point them out. I'd appreciate others' perspectives on the topics covered in the conference:

• Mehdi Assanioussi, http://www.gravity.physik.fau.de/events/tux3/assanioussi.pdf
• Norbert Bodendorfer, http://www.gravity.physik.fau.de/events/tux3/bodendorfer.pdf
• Goffredo Chirco, http://www.gravity.physik.fau.de/events/tux3/chirco.pdf *
• Andrea Dapor, http://www.gravity.physik.fau.de/events/tux3/dapor.pdf
• Beatriz Elizaga de Navascues, http://www.gravity.physik.fau.de/events/tux3/elizaga.pdf
• Muxin Han, http://www.gravity.physik.fau.de/events/tux3/han.pdf *
• Maximilian Hanusch, http://www.gravity.physik.fau.de/events/tux3/hanusch.pdf
• Marcin Kisielowski, http://www.gravity.physik.fau.de/events/tux3/kisielowski.pdf
• Ilkka Mäkinen, http://www.gravity.physik.fau.de/events/tux3/maekinen.pdf
• Mercedes Martin-Benito, http://www.gravity.physik.fau.de/events/tux3/martin.pdf
• Guillermo Mena Marugan, http://www.gravity.physik.fau.de/events/tux3/mena.pdf
• Tomasz Pawlowski, http://www.gravity.physik.fau.de/events/tux3/pawlowski.pdf
• Jorge Pullin, http://www.gravity.physik.fau.de/events/tux3/pullin.pdf
• Saeed Rastgoo, http://www.gravity.physik.fau.de/events/tux3/rastgoo.pdf
• Carlo Rovelli, http://www.gravity.physik.fau.de/events/tux3/rovelli.pdf *
• Giuseppe Sellaroli, http://www.gravity.physik.fau.de/events/tux3/sellaroli.pdf
• Jedrzej Swiezewski, http://www.gravity.physik.fau.de/events/tux3/swiezewski.pdf
• Francesca Vidotto, http://www.gravity.physik.fau.de/events/tux3/vidotto.pdf *
• Wolfgang Wieland, http://www.gravity.physik.fau.de/events/tux3/wieland.pdf *
• Edward Wilson-Ewing, http://www.gravity.physik.fau.de/events/tux3/wilson.pdf *
• Xiangdong Zhang, http://www.gravity.physik.fau.de/events/tux3/zhang.pdf

For convenience here's the list of 6 starred ones:
Goffredo Chirco, http://www.gravity.physik.fau.de/events/tux3/chirco.pdf *
Muxin Han, http://www.gravity.physik.fau.de/events/tux3/han.pdf *
Carlo Rovelli, http://www.gravity.physik.fau.de/events/tux3/rovelli.pdf *
Francesca Vidotto, http://www.gravity.physik.fau.de/events/tux3/vidotto.pdf *
Wolfgang Wieland, http://www.gravity.physik.fau.de/events/tux3/wieland.pdf *
Edward Wilson-Ewing, http://www.gravity.physik.fau.de/events/tux3/wilson.pdf *

 

[marcus]

From the looks of things, I'm not doing all that well. Of the 6 themes I started with only 3 (the even numbered ones it turns out) were represented at the conference:
2. refers to December 2014 paper by Haggard Han Kaminsky Riello (google "4D loop quantum gravity with a cosmological constant", part of the title of their paper) and February 2015 paper by Rovelli Vidotto ("compact phase space, cosmological constant, discrete time")
4. google "LambdaCDM bounce" for standard cosmology combined with matter bounce/Loop bounce.
6. google "planck star" for work by Barrau, Rovelli, Vidotto on prospects of seeing collapse rebound explosions

For example:
Goffredo Chirco, http://www.gravity.physik.fau.de/events/tux3/chirco.pdf *
Muxin Han, http://www.gravity.physik.fau.de/events/tux3/han.pdf * (theme 2)
Carlo Rovelli, http://www.gravity.physik.fau.de/events/tux3/rovelli.pdf * (theme 6)
Francesca Vidotto, http://www.gravity.physik.fau.de/events/tux3/vidotto.pdf * (theme 2)
Wolfgang Wieland, http://www.gravity.physik.fau.de/events/tux3/wieland.pdf *
Edward Wilson-Ewing, http://www.gravity.physik.fau.de/events/tux3/wilson.pdf * (theme 4)

AFAICS none of the talks dealt with the other themes, the odd numbered ones:
1. refers to Sep and Dec 2014 papers by Chamseddine Connes Mukhanov where quanta of both GR geometry and StdMdl matter seem to grow from the same algebraic root
3. google "flux formulation LQG" for Dittrich&Geiller new formulation of LQG, likely opening to the GR limit.
5. google "projective LQG" for massive work by Lanery&Thiemann reformulating LQG.

BTW Muxin Han gave a similar talk (same slide set) just this past week (10 March) on ILQGS. And the audio is online! This is connected with the HHKR paper where they use constant curvature simplexes to implement the cosmological curvature constant Lambda. Listening to the audio while reviewing the slides could help understand the HHKR (Haggard Han Kaminsky Riello) paper
http://relativity.phys.lsu.edu/ilqgs/han031015.pdf
http://relativity.phys.lsu.edu/ilqgs/han031015.wav

Chirco's talk is part of an important research initiative, to attain a general covariant version of statistical mechanics and thermodynamics. I should have included it earlier and will discuss it.
In a general covariant context there is no preferred time, no absolute notion of energy, no Hamiltonian, so how to do stat mech and thermodynamics, which require these things? It seems that statistical physics has to be rebuilt from the ground up. Analogs of the basic thermo ideas have to be constructed in the general covariant context. I would like to understand Chirco's slides better, and wish there were audio available to go with them.